Problem: The price of a particular item is reduced by successive discounts of $30\%$, $40\%$, and $50\%$. What is the selling price of the item after the three successive discounts, if it originally cost $\$200$?
A discount of $30\%$ means we pay $70\%=\frac{100-30}{100}=\frac{7}{10}$, a discount of $40\%$ means we pay $\frac{6}{10}$, and a discount of $50\%$ means we pay $\frac{5}{10}$. With successive discounts, we multiply the fractions. The selling price is $$\frac{7}{10}\cdot\frac{6}{10}\cdot\frac{5}{10}\cdot200=\frac{7}{10}\cdot\frac{3}{5}\cdot\frac{1}{2}\cdot200=\frac{7\cdot3\cdot10}{5}=7\cdot3\cdot2=\boxed{\$42}.$$